ALFRED P. SLOAN SCHOOL OF MANAGEMENT
"IMPROVING PRODUCTIVITY OF SERVICE BUSINESSES
WITH A NEW EFFICIENCY EVALUATION TECHNIQUE"
H. David Sherman
Sloan School of Management
Massachusetts Insitute of Technology
Revised October 1983
SSM Working Paper #1498-83 196-^
INSTITUTE OF TECHNOLOGY
50 MEMORIAL DRIVE
CAMBRIDGE, MASSACHUSETTS 02139
"IMPROVING PRODUCTIVITY OF SERVICE BUSINESSES
WITH A NEW EFFICIENCY EVALUATION TECHNIQUE"
H. David Sherman
Sloan School of Management
Massachusetts Insitute of Technology
Revised October 1983
SSM Working Paper #1498-83 i%3
How can a manager evaluate the productivity of a bank branch, a
hospital, or other service organization? A bank branch may have outstanding
profit performance based on a measure of the revenues earned on funds less
the costs of funds generated, and less the operating costs. This measure
does not, however. Indicate whether the branch Is using Its resources
efficiently or whether It could reduce Its operating costs and further
Increase profitability. Similarly, If one hospital provides patient care at
a cost of $300 per day and another provides patient care at $350 per day,
can a manager draw any conclusions about their relative productivity without
further considering the mix and nature of patient care provided? Measuring
the productivity of these and other service businesses requires techniques
that are more sensitive than accounting and ratio type measures and which
can explicitly consider the mix of service outputs produced. This article
explains how to apply a recently developed method for measuring and
improving the efficiency of service businesses. The technique, referred to
as Date Envelopment Analysis, has thus far been applied to banks, hospitals,
computer manufacturer field service organizations, and educational
institutions, as well as other service organizations.
The service sector of the U.S. economy has been estimated to account for
over 60% of Gross National Product and employment. Add to this the service
components of manufacturing firms and it is clear that service sector
productivity is a substantive issue as suggested in the following examples.
• Over 20% of computer manufacturer revenues are generated from
customer service activities. These companies need to monitor and
manage the service aspect of their business to help achieve their
growth and profitability goals.
• Hospital cost Increases are a serious and continuing concern.
Their management are Increasingly accountable for assuring
efficient delivery of health care services.
• Public sector organizations face continued taxpayer pressures to
maintain service at or above current levels but at a lower cost.
Although the need for managerial methods to enhance productivity in the
service industry Is apparent, techniques to accomplish these Improvements
have not been developed as they have for the manufacturing sector.
Service business efficiency is often more difficult to evaluate than
manufacturing business efficiency because the efficient amount of resources
required to produce service outputs is difficult to determine. The standard
or efficient cost of a manufactured product can generally be determined with
some precision. This manufacturing standard can be used to identify
operating inefficiencies by analyzing differences between actual cost and
standard costs through classical cost accounting variance analyses. (1)
Service organizations have not generally developed standard cost estimates
of outputs. One reason for this is that the specific resources required to
provide a specific service output are difficult to identify. (This, of
course, is also true of manufacturing organizations that produce highly
customized products.) Another reason may be that those being evaluated
against a standard cost would not accept or be able to agree on a standard
because of the professional judgement involved in providing each type of
service. For example, the professional might convincingly argue that no two
audits, heart operations, or customer service calls are alike, so that no
standard or efficient input level can be identified as a basis for
evaluating the efficiency of producing such services.
Another approach to evaluate service productivity is to develop a series
of output to input ratios such as full-time equivalents per service unit.
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dollars per transaction, etc. The Idea Is that units with higher costs per
transaction would be potentially less efficient than those with lower
costs. For example, a measure of bank branch operating efficiency that
might be used Is the ratio of cost per teller transaction. The branch with
the higher cost per teller transaction may be less efficient.
Alternatively, this higher cost per transaction may be due to a more complex
mix of transactions. That Is, a branch which primarily opens new accounts
and sells certificates of deposit would require more resources per
transaction than another branch that primarily processes less complex
transactions such as deposits and check cashing. In short, the problem with
these ratio measures is that the mix of outputs is not explicitly considered.
Profitability, return on investment, and other financial ratios are
highly relevant as performance measures of many service businesses, but they
are not sufficient to evaluate operating efficiency. For example, a bank
branch may be profitable when profit reflects the Interest and the revenues
earned on funds generated by a branch less the cost of these funds and less
the costs of operating the branch. This profit measure does not, however.
Indicate whether the resources used to provide customer services are being
managed efficiently. The branch that processes a high proportion of cash
withdrawals and other non-fund-generating services may have higher operating
costs and lower profitability than one which processes a lower proportion of
nonfund generating transactions. Nevertheless, the less profitable branch
may be more efficient using its personnel and other Inputs than the more
profitable branch. In this Instance, the more profitable branch may be able
to provide its same service level with fewer inputs which would result in
lower operating costs and yet greater profitability. For non-profit
organizations, profit maximization Is generally a secondary consideration
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and the need for other types of performance measures Is even more acute than
In the for-profit service businesses.
There are also differences within the service sector organizations that
need to be considered in adopting performance evaluation techniques.
Professional service organizations, such health care, management consulting,
and accounting firms experience greater difficulty defining efficient
input/output relationships than other types of service organizations where
labor inputs are highly controlled and standardized, such as fast food
restaurants. This is most evident when one examines a text on operations
management in service businesses (see for example ). The management
techniques that are described in such a text tend to be extremely useful in
managing a McDonald's restaurant but are of only marginal value in running a
health care clinic. In contrast, texts discussing management of nonprofit
service organizations such as  reflect keen awareness of the difficulty
of measuring outputs and determining the efficient level of inputs required;
however, solutions to these problems are not provided in any detail.
Recently, a new technique was developed which has the ability to compare
the efficiency of similar service organizations by explicitly considering
their use of multiple Inputs (resources) to produce multiple outputs
(services). The technique, referred to as Data Envelopment Analysis (DEA) ,
circumvents the need to develop standard costs for each service provided.
It provides a measure of efficiency that is explicitly sensitive to the
output mix and is consequently more comprehensive and reliable than use of a
set of operating ratios and profit measures. Data Envelopment Analysis
compares a set of service organizations and identifies units that are
relatively inefficient, the magnitude of the inefficiency, and alternative
paths to reduce the identified inefficiencies. Management can use DEA to
Identify the inefficient units and the magnitude of the inefficiency. In
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addition, DEA can help assess plans to remedy and reduce these
inefficiencies. This can lead to (1) a reduction In the cost of operations
or (2) an increase in the services provided without an increase in the level
of resources utilized by the inefficient units*
DEA is a linear programming technique originally developed by Charnes,
Cooper, and Rhodes (, , and ) to evaluate nonprofit and public
sector organizations and has subsequently been found to be a valuable tool
in application to a variety of corporate service type organizations. DEA
has been applied to hospitals , primary and secondary educational
Institutions [6j, , court systems , armed forces recruiting offices,
bank branches , and customer service offices of a computer manufacturer.
The following section briefly describes and Illustrates how DEA works.
The appendix provides details about how DEA can be applied using any
standard linear programming package. The subsequent section describes how
this has been applied to hospitals and bank branches. The final section
discusses the strengths and limitations of DEA and how management can use
DEA to evaluate and Improve operating efficiency of service organizations.
Data Envelopment Analysis - How it Works and How to Interpret the Results
Use of DEA to evaluate efficiency will be illustrated with a simplified
bank branch example where there is only one type of transaction processed
and two types of resources used to processes these transactions - bank
tellers and supplies. This example was selected because it lends itself to
an easily visualized graphic description. In addition, this example is
simple enough to be analyzed without DEA, so that the results can be
compared to an independent analysis of efficiency. Note that DEA is most
valuable in complex situations where (1) there are multiple outputs and
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Inputs that cannot readily analyzed with other techniques like ratios, and
(2) where the number of service organization units being evaluated are so
numerous that management cannot afford to evaluate each unit In depth. For
example, an actual bank application Included 18 different transaction types
as output measures and 14 branches were to be evaluated. DEA was used to
help direct management's efforts to Improve efficiency of units that were
first identified as inefficient with this technique.
Assume that there are five bank branches (Bl, B2, B3, B4, and B5) that
each process 1,000 transactions such as deposits by jointly using two
inputs, tellers measured in labor hours (H) and supplies measured in dollars
(S) during one common time period (week, month, year, etc.). The amount of
inputs are summarized in table 1.
The problem facing the manager is to identify which of these branches are
inefficient and the magnitude of the inefficiency. This Information could
be used to locate the branches that require remedial management action, to
reward the more efficient managers, and/or to determine the management
techniques that are used in the more efficient branches so that they can be
transferred to less efficient branches to Improve their operating
efficiency. While the manager can observe the number of transactions
processed and the amount of resources (H and S) used, the manager does not
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know the efficient output/input relationship. That is, the efficient amount
of labor and supplies needed for each transaction is not readily
determinable. Hence, the problem might be visualized as in Figure 1.
In this example, it can be observed that Bl and B2 are relatively
inefficient. Bl produced the same output level as B4 but used 100 more
supply dollars (S) than were used by B4. B2 also produced the same output
level as B4 but achieved this through the use of 10 more Teller labor
hours. With the information available in table 1, it is not possible to
determine whether B3, B4 or B5 are more or less efficient. While
information about relative prices might allow one to rank B3, B4 and B5, the
finding that Bl and B2 are inefficient would not change. That is, Bl and B2
should be able to reduce inputs without reducing outputs regardless of the
price of the inputs.
Data Envelopment Analysis compares each service unit with all the other
service units and identifies those units that are operating inefficiently
compared with other units' actual operating results. It accomplishes this
by locating the best practice units, (units that are not less efficient than
other units being evaluated) and measures the magnitude of inefficiency
compared to the best practice units. The best practice units are relatively
efficient and are Identified by a DEA efficiency rating of E = 100%. The
inefficient units are identified by an efficiency rating of less that 10 0%
(E < 100%).
The DEA techniques and the data needed to apply DEA are described in
Exhibit I. DEA is applied to the example in Table 1 in Exhibit I.
DEA first provides the type of information summarized in table 2.
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Problem: Which are the inefficient branches and what is the magnitude
of the inefficiency present?
20 units of H
300 units of S
30 units of H
200 units of S
40 units of H
100 units of S
20 units of H
200 units of S
10 units of H
400 units of S
- 8 -
Table 2 Indicates that DEA Identified the same inefficient branches
that were identifiable through observation of the data. Bl and B2 have
efficiency ratings below 100% which identifies them as inefficient. In
addition, DEA further focuses the managers attention to a subgroup of the
bank branches which are referred to as the efficiency reference set in Table
2. This efficiency reference set includes the group of service units
against which each Inefficient branch was most directly found to be
inefficient. For example, Bl was found to have operating Inefficiencies in
direct comparison to B4 and B5. The value in parenthesis in Table 2
represents the relative weight assigned to each efficiency reference set
member to calculate the efficiency rating (E). (This corresponds to the
non-zero shadow prices of the constraints which is directly available from
the DEA linear program output.) More specific information about the nature
and magnitude of the inefficiency present are available from the DEA results
as is illustrated in Figure 2 using B2 as an example.
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All branches produce 1000 units of a single transaction
type (T) using the following amounts of Teller Hours (H)
Supply Dollars (S) .
y (25.7, 171)
Teller Hours (T)
DEA has determined that the relatively efficient bank branches among the
five are B5, B4, and B3. This can be represented In this simple case by the
solid line in Figure 2 which locates the units that used the least amount of
inputs to produce their output level. DEA indicates that B2 is inefficient
compared to the line connecting B4 and B3; B2 is 85.7% efficient compared to
B4 and B3. This means that one way for B2 to become efficient is to reduce
its inputs to 85.7% of its current level which would move B2 onto this
relatively efficient production segment at point e in Figure 2, which
reflects use of 25.7 teller hours (.857 X 30) and use of 171 supply dollars
(.857 X 200). DEA provides information to complete the calculation
suggested in Figure 2. This Is Illustrated in Table 3.
Table 3 indicates that a mixture of operating techniques utilized by B3
and B4 would result in a composite hypothetical branch that processes the
same amount of transactions (1,000) processed by B2 but also requires fewer
inputs than wejre used by B2. Hence, by adopting a mixture of the actual
technique used by B3 and B4 , B2 should be able to reduce teller hours by 4,3
units and supply dollars by 29 units without reduction in its output level.
A similar calculation can be completed for each inefficient unit located via
a DEA analysis.
Management is also provided with alternative paths to Improve efficiency
of B2. One path suggested in Table 3 is for B2 to reduce H by 4.3 units and
reduce S by 29 units. Other paths are ascertainable from the DEA output as
follows: DEA calculates a relative value for each input and output (the
v^ and V2 values that result in the efficiency rating as noted in
Exhibit I). For branch Bl, this value is 1.436 for teller hours (H) and
0.286 for supply dollars (S). This means that for each unit of reduced
teller hours, the efficiency of B2 increases by 1.43%; and for each unit
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OUTPUTS AND OUTPUTS AND
INPUTS OF B3 INPUTS OF BA
REFERENCE SET FOR
SERVICE UNIT B2
(.2857) X 1000 + (.7lA3)x 1000
The composite for B2 can then be compared with the Inefficient unit B2
OUTPUTS AND INPUTS
COLUMN 2 -
OUTPUTS AND INPUTS
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decrease In supply dollars, the efficiency of B2 will Increase by 0.286%.
For B2 to become relatively efficient, it must increase its efficiency
rating by 14.3percentage points. Hence, B2 can become efficient by
decreasing H by 10 hours (10 hours X 1.43% = 14.3%) or by decreasing S by 50
units (50 X 0.286% = 14.3%) or by some combination of these reductions in H
and S. The choice of which path to follow would, of course, be based on
management's evaluation with respect to cost, practicality, and feasibility
under the particular organization's circumstances.
At this point it must be reemphasized that DEA results are most useful
when there are multiple outputs and inputs and where the type of intuitive
analysis that could be applied to verify the DEA results in the above
example would not be possible. Nevertheless, the efficiency rating, the
efficiency reference set, the analysis as performed in Table 3, and the
ability to determine alternative paths that would make an inefficient unit
efficient would all be readily available.
How Can A General Manager Understand All This Technical Material?
Business application of DEA to banks, hospitals, and customer service
organizations suggests that the presentation along the lines of Table 3 is
one of the most direct ways to summarize and explain what DEA has achieved
and the implications to management. The interpretations of DEA results tend
to proceed in the following order:
• The efficiency ratings are generated as in Table 2. Units that are
efficient (E = 100%) are relatively and not strictly efficient.
This means that there is no other unit that is clearly operating
more efficiently than this unit but it is possible that all units
including these relatively efficient units can be more efficiently
operated. The efficient branches, B3, B4, and B5, therefore,
represent the best practice but not necessarily the best possible
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Inefficient units are located with efficiency rating of
E < 100%. These units, Bl and B2, are strictly Inefficient
compared to all the other units and are the ones where remedial
action by management should be considered. In fact, the
inefficiency identified with DEA will tend to understate rather
than overstate the inefficiency present.
The efficiency reference set indicates the relatively efficient
units against which the inefficient units were most clearly
determined to be inefficient. The presentation In Table 3
summarizes the magnitude of the inefficiencies located by comparing
the inefficient unit with its efficiency reference set.
The results in Table 3 might be summarized as follows:
32 has been found to be relatively less efficient than a composite
of the actual output and input levels of B3 and B4. If a
combination of operating techniques used in B3 and B4 were
transferred to inefficient unit B2 , B2 should be able to reduce the
amount of H used by 4.3 units and reduce the amount of S used by 29
units while providing the same level of services. Other methods to
Improve efficiency are also identifiable via DEA, such as were
described above, which should also be considered by management in
designing a program to improve the efficiency of each inefficient
unit Identified by DEA.
Comparison of Teaching Hospitals' Medical Surgical (MS) Area
Area Cost Per
A, C, E
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Application and Use of PEA as Management Control Tool
to Improve Operating Efficiency
A set of teaching hospitals were compared and evaluated using DEA. The
Inputs were Identified as bed days available, full-time equivalents of
non-physic Ian staff, and supply dollars. Outputs Included measures of
number of Interns, residents and nurses trained and the number of bed days
of care administered for each patient type.
The DEA results located a set of Inefficient hopsltals not otherwise
Identifiable using ratio analysis techniques (e.g., cost per day, cost per
patient), the method used by the local regulatory agency which needs this
type of data to affect hospital reimbursement rates. The DEA results were
found to be meaningful and accurate by a panel of hospital experts familiar
with these hospitals. Moreover, management of one inefficient hospital
acknowledged the inefficiencies identified with DEA particularly with
respect to their use of excessive personnel and bed days.
The DEA results focusing on the medical/surgical areas of a group of
these hospitals are in table A along with the ratios of cost per patient day
of care. The cost per patient day is a typical example of ratio which might
be used to locate high and low cost hospitals. Note that there is no
objective means of establishing a cutoff cost level which separates the more
and less efficient hospitals. The local regulatory agency defined
potentially inefficient hospitals as those which have costs over one
standard deviation above the mean. This "rule of thumb" identifies only
hospital C as inefficient. In addition, there is no way to determine if
this represents use of excess inputs or payment of higher prices for their
inputs. In addition, hospital C may have higher costs primarily because it
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treats more complex patient Illness or provides greater amounts of teaching
services. These are typical problems associated with financial and
DEA identified two hospitals, D and G, as inefficient in their use of
inputs to produce the actual mix of patient care and teaching services
provided. Note that these hospitals would have gone unnoticed using
ratios. Unlike the ratios, the use of DEA allowed for explicit
consideration of case mix and teaching outputs. DEA Identified the use of
excess amounts of Inputs in specific hospitals without the need for an
arbitrary or subjective decision rule as to which units are inefficient.
Correcting these inefficiencies would result in yet lower costs for
hospitals D and G.
Management of hospital D studied the detailed DEA results and agreed
that they had an excessive number of beds and personnel compared with the
other hospitals. They planned to reduce the number of beds by 19, freeing
up space for other uses. They also determined that personnel levels were
excessive by 5.4 full-time equivalents but chose not to make any reductions
here because their policy was to maintain high personnel levels to provide
more personalized care. The planned reduction in the number of beds was
reevaluated using DEA. This indicated that this hospital would still be
rated as inefficient but with a higher rating of 96% compared with the
original level of 88%. If they also reduced personnel by the 5.4 units they
identified, their DEA efficiency rating would have increased to 100.
Hence, DEA provided a basis for improving productivity by reducing the
number of beds and it indicated reduction in personnel were possible without
affecting output levels which could further reduce costs. In this case, DEA
also helped to clarify the cost of the intended inefficiency or slack and
challenges management to justify this cost. Thus, DEA provided insights
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about Inefficiencies not available from ratio analysis. Nevertheless, the
questions raised about the cost per patient day and other similar ratios are
also relevant. Hence, DEA is a complement to, rather than a substitute for,
other types of analysis.
Savings Bank Application
Branches of a savings bank were compared using DEA to assess their
operating efficiency. The bank's head office management developed a branch
profit measure which was considered to be useful in evaluating a number of
dimensions of branch performance. This profit measure did not, however,
provide information about branch resource utilization because the
transaction mix was not considered and the profit was mostly a measure of
earnings from funds generated by each branch. Hence, the potential benefits
of applying DEA were of interest. The process began by identifying relevant
outputs and inputs of a branch. Inputs included personnel full-time
equivalents and supply costs. Outputs were identified as the number of each
of seventeen transaction types, including for example, opening new accounts,
withdrawals, deposits and issuing savings bonds.
DEA was first used to identify inefficient branches and the magnitude of
input reductions that were possible. This result was not apparent from
other evaluation techniques used in the bank including profitability
measures and operating ratios such as cost per transaction and number of
transactions per FTE. DEA indicated that six of the 14 branches were
inefficient. Most of the branches identified as inefficient were consistent
with head office management expectations based on their view of quality of
the managers in these branches. However, one branch identified as
inefficient was a complete surprise to management. This information was
particularly useful because it quantified the operating inefficiencies which
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were only vaguely apparent to management based on their Intuition about the
branch managers. Moreover, this insight was obtained without the need to
Involve branch managers in any part of the process, since the output and
input data were already available at the head office.
DEA first alerted management to the branches that were inefficient and
the magnitude of the inefficiency. This allowed management to assess the
potential benefits of taking remedial action. Beyond this, DEA specified
the efficient branches against which the inefficient branches should be
compared to understand and locate the source of the inefficiencies. By
comparing the operating techniques in the narrowed set of efficient and
inefficient branches, management could identify the techniques which require
improvement and the techniques which should be transferred from the more
efficient branches to the less efficient branches to improve the latter 's
Use of DEA alerted management to cost saving opportunities that were not
apparent with other techniques and it helped management to allocate their
time and remedial efforts to areas where operating weaknesses were now known
to exist. Based on favorable reaction to this effort, bank management
further proposed to use DEA to compare their branches with those of another
bank they were acquiring to determine if there were opportunities for
improving operations through the transfer of good branch management
techniques from the original to the newly acquired branches or vice versa .
The above examples illustrate the use of DEA to compare organizations
that jointly produce a set of similar service outputs with a set of inputs.
This can readily be applied across organizations in the non-profit sector
where data are publicly available as in the teaching hospital example.
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Corporate applications of PEA will tend to emphasize cases where
management wants to evaluate and Improve efficiency of a set of offices
providing similar services as In the bank example . It would also be
possible to compare Independent competing firms using DEA, but this type of
data would generally be difficult to obtain due to the condlfentlallty of
detailed operating data. Consequently, the corporate applications will
generally be limited to comparison of multiple service offices such as bank
branches, customer services officers, multi-office CPA firms, and Insurance
How Would Management Apply DEA
Step 1 ; Management would Identify the units for which a DEA efficiency
evaluation would be of interest. This would generally be a set of units
that provide similar services for which management wants to evaluate
performance and Improve operating efficiency.
Step 2 ; The relevant outputs and inputs of the units to be evaluated
would be identified by management and measured for a representative period
of time (year, quarter, month). The relevant outputs are those services and
other activities that the unit is responsible for to achieve its business
purpose. The inputs are those resources that are required to produce the
designated outputs. Field applications of DEA have indicated that this
process of output and input indentlficatlon In itself is often useful to
managers, as the outputs and Inputs are frequently not explicitly identified
or understood. In addition, some of the relevant outputs and Inputs may not
have been measured or captured In the management Information system of the
firm. The absence of data on relevant outputs and Inputs has tended to
raise questions about the adequacy of the information system, since this
type of input-output data are needed to assess operating performance
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regardless of the techniques that may be used. Generally, the outputs used
should be related to the Inputs selected in that an efficient unit should be
expected to respond over time to an increase or decrease in outputs with a
corresponding increase or decrease in the various inputs.
If all the relevant outputs and inputs are not included in the DEA
analysis, the DEA results will have to be reviewed for any bias that might
result. For example, the DEA application to hospitals excluded a measure of
the quality of services. Such use of DEA requires that the results be
reconsidered to determine if the inefficient hospitals' quality of care
exceeds the efficient hospitals' quality of care by a large enough margin to
compensate for the DEA calculated inefficiency. The hospital application
that addressed this issue found that quality of care was not a compensating
factor. Other applications of DEA may, however, require some qualification
if certain relevant input or output measures are excluded.
Step 3 : DEA would be applied to the output and input data and the
results would be analyzed to help management locate and remedy operating
inefficiencies. Generally, management will not have seen results similar to
DEA and these results will tend to provide insights not available from other
widely used analytical techniques such as ratio analysis. Management might
begin by considering whether the location and magnitude of inefficiencies
are consistent with their prior view of the operations of the service units
being evaluated. This may raise questions about the completeness and
representativeness of the output and input data.
The inefficient units would then be further studied and compared with
their efficiency reference set units to evaluate the cause and
controllability of the identified inefficiencies. In some cases, the
Inefficiencies present may represent intended slack built into a unit or
special circumstances which do not permit improvements in operating
- 20 -
efficiency. In this circumstance, DEA helps to understand the cost of this
Inefficiency and no further managerial actions may be warranted. When the
inefficiencies are found to be associated with the systems and managerial
techniques used in these units, remedial action to improve efficiency would
Insights from DEA direct management's attention to aspects of operations
which are highly likely to benefit from remedial action. In contrast to
other techniques, DEA evaluates units by explicitly and simultaneously
considering the multiple Inputs used to produce multiple outputs and without
the need to know the efficient input/output relationships. Although DEA
does not actually specify the remedial action needed, it narrows the focus
of management's Investigation to the inefficient units and their efficiency
reference set. Through this process, DEA helps allocate management support
to areas where weaknesses are known to exist and helps management identify
ways in which management techniques can and should be improved.
Dynamic Analysis with DEA
In addition to the static one year or period analysis such as was
completed for the bank branches and hospitals, DEA can monitor and thereby
help control the level of operating efficiency over time. DEA can be run
with multiple period information (quarters, years, etc.) for individual
ogranization units or for each of a set of units being compared to determine
if units are becoming more or less efficient with respect to other units and
with respect to themselves over time. The use of DEA for successive periods
would suggest whether the previously inefficient units have become
relatively efficient through remedial actions taken and DEA would help
locate other units that have become relatively inefficient.
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DEA suggests a variety of paths to reduce Identified inefficiencies.
Management may find that yet other paths are more feasible and/ or less
costly. DEA can be reapplied to the same set of units after adjusting the
outputs and inputs to reflect management's plan to improve efficiency. DEA
would indicate whether the changes anticipated will reduce the
inefficiencies sufficiently for management purposes.
What are the Costs of Using DEA?
DEA can be run and interpreted with very modest amounts of training by
individuals that have access to and are able to run any standard linear
program package. Once the input and output data are available, the
Incremental cost of obtaining a DEA evaluation Is minimal when such a linear
program package is on hand.
The costs of Identifying and collecting the output and input data not
already available may be significant. While this cost might be incurred In
conjunction with the DEA process, it is frequently considered valuable as an
end in itself and is often an indicator of Infonnation gaps about aspects of
operation which should be remedied regardless of the analytic techniques
that will be used.
The area where significant costs are Involved are in the followup to
evaluate the way inefficiencies can be reduced and In identifying the
techniques that exist In relatively efficient units that should be
transferred to less efficient units. The value of DEA In this context is
its ability to narrow management's focus to areas where inefficiencies are
known to exist and where benefits of managerial action are likely to result
In productivity Improvements. Hence, these costs are likely to lead to
benefits which compensate for costs of the DEA process.
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In summary, the class of service organization which can be evaluated
using DEA are those which produce multiple services with multiple Inputs,
where the efficient output/input relationships are not known or are
difficult to Identify, and where several units can be compared to evaluate
relative performance. For this class of service units, DEA is a useful
technique for locating ways to Improve efficiency and profitability and can
be a valuable complement to other management control tools and techniques
used within these organizations. Considering the very few techniques
available to evaluate and Improve service business productivity, it would be
reasonable for any manager of such an organization to consider the use of
DEA to assist management in improving the productivity of its organization.
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DEA is a linear programming technique that Is structured as follows:
Find the set of coefficients u's and v's that will give the highest possible
efficiency ratio of outputs to inputs for the service unit being evaluated
(Eg): i.e., the objective function is:
(la) Maximize E = "l°le '*' "2*^2
u, 0, + u_0^ + ... u
1 le z 2e r re
v. I, + v„I- + ... v I
1 le 2 2e m me
(Maximize the efficiency rating E for service unit e)
subject to the constraint that when the same set of u and v coefficients is
applied to all other service units being compared, that no service unit will
be more than 100% efficient as follows:
Service Unit 1 " l°ll "^ "2°21 '^ ' " "r°re <100%
^1^11 + ^2^21 + ••• \^ml
Service Unit 2 " 1^12 ^ "2^22 "^ -' "^ "r°r2 £lOO%
Vie ■'^2 02e "^ * ' ' + Vm2
Service Unit e " l°le "^ "2°2e "^ '•• "r"re <100%
(as in (la)) v^I^^ + v^O^^ + ... v^O^^
Service Unit J " l"lj "^ "2°2j "^ •- "^ "r°rj <100%
^l^lj + ^2^j + ••• + Vmj
and such that the coefficient values are positive and non-zero.
v, , . . . V <
u, , . . . u < 0,
The data required to apply DEA is the actual observed outputs produced
(0^ ••• Of) and actual inputs used (I^^ ... I„,) during one time
period for each service unit in the set of units that are being evaluated.
Hence, I^a is the observed amount of the mth input used by the jth service
unit, and Oj. ^ is the amount of rth output produced by the jth service unit.
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If the value of Eg for the service unit being evaluated Is less than
100%, then that unit Is relatively Inefficient and there Is the potential
for that unit to produce the same level of outputs with fewer Inputs. (See
, , , and  for further details on the theory and application of
Assume that the DEA evaluation would begin by evaluating the efficiency
of bank branch B2 . The problem would be structured as follows, based on the
DEA model above and using the data in table 2:
Calculate the set of values for uj, v^, V2 that will give B2 the
highest possible efficiency rating,
„ , ^ ^ tu(lOOO) [This is the linear program
Maximize E„™ = I ^v.i ^t c ^t ^
^2 v.^(3Q) + V2(200) objective function ]
subject to the constraint that no service unit can be more than 100%
efficient when the same values for u^, vj^ and V2 are applied to each
Bi "i^^QO") <100%
v^(20) + V2(300)
B2 "i^^QQQ^ <100%
Vj^OO) + V2(200)
B3 "l^^PQO^ <100%
Vj^CAO) + v^ClOO)
B4 "l^^QQO) < 100%
Vj^(20) + V2(200)
B5 "l^^°°Q^ <100%
^1^1°^ + ^400)
and subject to the constraint that v^, V2 and u^ are all greater than
For B2, DEA calculates its efficiency rating to be 85.7% and the value
for ui = 1, vj^ = 1.436 and V2 - 0.286. DEA would be rerun for each
branch in the objective function.
The results from running DEA fives times with each of the units in the
ojectlve function is summarized in Table 2.
- 25 -
1. Anthony, R. N., and J. S. Reece, Accounting, Text and Cases, sixth
edition, Homewood, Illinois: Richard D. Iirwln, Inc. 1979, Chapters
17 and 23.
2. Sasser, W. F., R. P. Olsen, and D, D. Wyckoff, Management of Service
Operatlngs, Test, Cases and Readings , Boston, Massachusetts: Allyn
and Bacon, Inc. 1978.
3. Anthony, R. N., and R. E. Herzllnger, Management Control In Nonprofit
Organization, revised edition, Homewood, Illinois: Richard D.
Irwin, Inc., 1980.
4. Charnes, A., W. W. Cooper and E. Rhodes, "Measuring the Efficiency of
Decision Making Units," European Journal of Operations Research,
Vol. 2, No. 6, November 1974, pp. 429-444.
3. Charnes, A., W. W. Cooper and E. Rhodes, "Short Communication:
Measuring Efficiency of Decision Making Units," European Journal of
Operations Research , Vol. 3, No. 4, July 1979, p. 339.
6. Charnes, A. W. W. Cooper, and E. Rhodes, "Evaluating Program and
Magerlal Efficiency: An Application of Data Envelopment Analysis
to Program Follow Through," Management Science , Vol. 27, No. 6,
June 1981, pp. 668-697/
7. Sherman, H. D., "A New Approach to Evaluate and Measure Hospital
Efficiency," Sloan School of Management Working Paper #1427-83,
8. Bessent, A., W. Bessent, J. Kennlngton, and B. Regan, "An Application of
Mathematical Programming to Assess Productivity In the Houston
Independent School District," Management Science , December 1982.
9. Lewln, A. Y. , and R. C. Morey, "Evaluating Administrative Efficiency of
Courts," Omega , (forthcoming).
10. Sherman, H. D. and F. Gold, "Evaluating Operating Efficiency of
Service Businesses with Data Envelopment Analysis - Empirical Study
of Bank Branch Operations," Sloan School of Management Working
Paper #1444-83, June 1983.
11. Charnes, A., W. W. Cooper and H. D. Sherman, "A Comparative Study of
Data Envelopment Analysis and Other Approaches to Efficiency
Evaluation and Estimation," Center for Cybernetic Studies Research
Report #451, University of Texas at Austin, November 1982.
i+ 2 2 1 u 3 2 ^
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